How to extrude a face parallel to another?
The fast, inaccurate way


Select one of the upper edges and the lower edge, which you want to connect.
Subdivide W > S
Use the edge / vertice slide by pressing G > G
Enable the Even checkbox in the edge slide operation settings.
If necessary enable the Flipped checkbox in the edge slide operation settings.
Adjust the Factor slider estimating the slide position closest to the upper vertex.
Merge the upper vertices.




The slow, accurate way


Delete the face, which you want to split with the edge (loop).
Select the edge, which you want your new edge to be parallel to.
Go into Normal transform orientation mode, then (in the Properties Panel under Transform) press the + icon.  This will add the orientation of the edge as a possible transformation orientation.
Place a new vertex by subdividing the lower edge.
Snap the 3D cursor to the upper vertex, from which you want the edge loop to start.
Enable 2D Cursor as Pivot Point.
Select the vertex on the lower edge and scale it to 0 (with the 2D cursor as a pivot point). Limit the scale operation to the X and Z axis. Select the transform orientation of the edge, which we added earlier.
Make the new faces.